JEE Main 2025 (Online) 23rd January Morning Shift

A radioactive nucleus $\mathrm{n}_2$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus $n_1$. If initial number of both nuclei are the same, what is the ratio of number of nuclei of $n_2$ to the...

Identify the valid statements relevant to the given circuit at the instant when the key is closed.

A. There will be no current through resistor $R$.
B. There will be maximum current in the connecting wires.
C. Potential difference between ...

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residua...

Consider a moving coil galvanomenter (MCG):
A. The torsional constant in moving coil galvanometer has dimensions $\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$
B. Increasing the current sensitivity may not necessarily increase the voltage se...

A sub-atomic particle of mass $10^{-30} \mathrm{~kg}$ is moving with a velocity $2.21 \times 10^6 \mathrm{~m} / \mathrm{s}$. Under the matter wave consideration, the particle will behave closely like $\qquad$ $\left(\mathrm{h}=6.63 \times 1...

Regarding self-inductance:
A. The self-inductance of the coil depends on its geometry.
B. Self-inductance does not depend on the permeability of the medium.
C. Self-induced e.m.f. opposes any change in the current in a circuit.
D. Self-indu...

In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of $8 \mathrm{~A} / \mathrm{s}$. At an instant when R is $12 \Omega$, the value of the current in the circuit will be...

The electric field of an electromagnetic wave in free space is $\overrightarrow{\mathrm{E}}=57 \cos \left[7.5 \times 10^6 \mathrm{t}-5 \times 10^{-3}(3 x+4 y)\right](4 \hat{i}-3 \hat{j}) N / C$.
The associated magnetic field in Tesla is

Refer to the circuit diagram given in the figure. which of the following observations are correct?
A. Total resistance of circuit is $6 \Omega$
B. Current in Ammeter is 1 A
C. Potential across $A B$ is 4 Volts.
D. Potential across CD is 4 V...

A positive ion $A$ and a negative ion $B$ has charges $6.67 \times 10^{-19} \mathrm{C}$ and $9.6 \times 10^{-10} \mathrm{C}$, and masses $19.2 \times 10^{-27} \mathrm{~kg}$ and $9 \times 10^{-27} \mathrm{~kg}$ respectively. At an instant, t...

The electric flux is $\phi=\alpha \sigma+\beta \lambda$ where $\lambda$ and $\sigma$ are linear and surface charge density, respectively. $\left(\frac{\alpha}{\beta}\right)$ represents

A point particle of charge $Q$ is located at $P$ along the axis of an electric dipole 1 at a distance $r$ as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are mad...

Given a thin convex lens (refractive index $\mu_2$ ), kept in a liquid (refractive index $\mu_1, \mu_1<\mu_2$ ) having radii of curvatures $\left|R_1\right|$ and $\left|R_2\right|$. Its second surface is silver polished. Where should an obj...

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness ' $h$ ' in terms of the angle of incidence ' $i$ ' and angle of refraction ' $r$ ', if the glass slab is placed in air medium?

A spherical surface of radius of curvature $R$, separates air from glass (refractive index $=1.5$ ). The centre of curvature is in the glass medium. A point object ' $O$ ' placed in air on the optic axis of the surface, so that its real ima...

Match the List - I with List - II

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A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet i...

An ideal gas initially at $0^{\circ} \mathrm{C}$ temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is $3 / 2$, the change in temperature due to the...

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is ̱_______ km .

Given below are two statements:
Statement I: The hot water flows faster than cold water
Statement II: Soap water has higher surface tension as compared to fresh water.
In the light above statements, choose the correct answer from the option...

A solid sphere of mass ' $m$ ' and radius ' $r$ ' is allowed to roll without slipping from the highest point of an inclined plane of length ' $L$ ' and makes an angle $30^{\circ}$ with the horizontal. The speed of the particle at the bottom...

A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y \pi \times 10^{-2} \mathrm{~s}$, where the value of...

The position of a particle moving on $x$-axis is given by $x(t)=A \sin t+B \cos ^2 t+C t^2+D$, where $t$ is time. The dimension of $\frac{A B C}{D}$ is

Two particles are located at equal distance from origin. The position vectors of those are represented by $\vec{A}=2 \hat{i}+3 n \hat{j}+2 \hat{k}$ and $\bar{B}=2 \hat{i}-2 \hat{j}+4 p \hat{k}$, respectively. If both the vectors are at righ...

A force $\mathrm{f}=\mathrm{x}^2 \mathrm{y} \hat{\mathrm{i}}+\mathrm{y}^2 \hat{\mathrm{j}}$ acts on a particle in a plane $\mathrm{x}+\mathrm{y}=10$. The work done by this force during a displacement from $(0,0)$ to $(4 \mathrm{~m}, 2 \math...